Question: $h(t) = -6t^{2}+3t-5(g(t))$ $g(t) = 4t$ $f(n) = -2n-4(g(n))$ $ g(h(-5)) = {?} $
Explanation: First, let's solve for the value of the inner function, $h(-5)$ . Then we'll know what to plug into the outer function. $h(-5) = -6(-5)^{2}+(3)(-5)-5(g(-5))$ To solve for the value of $h$ , we need to solve for the value of $g(-5)$ $g(-5) = (4)(-5)$ $g(-5) = -20$ That means $h(-5) = -6(-5)^{2}+(3)(-5)+(-5)(-20)$ $h(-5) = -65$ Now we know that $h(-5) = -65$ . Let's solve for $g(h(-5))$ , which is $g(-65)$ $g(-65) = (4)(-65)$ $g(-65) = -260$